1809 words - 8 pages

NATIONAL SENIOR CERTIFICATE

GRADE 12

MATHEMATICS P1 NOVEMBER 2014

MARKS: 150 TIME: 3 hours

This question paper consists of 10 pages and 1 information sheet.

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Mathematics/P1

2 NSC

DBE/November 2014

INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. 3. This question paper consists of 12 questions. Answer ALL the questions. Number the answers correctly according to the numbering system used in this question paper. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers. Answers only will not necessarily be awarded full ...view middle of the document...

1 Given the quadratic sequence: – 1 ; – 7 ; – 11 ; p ; … 3.1.1 3.1.2 3.1.3 Write down the value of p. Determine the nth term of the sequence. The first difference between two consecutive terms of the sequence is 96. Calculate the values of these two terms. (2) (4)

(4)

3.2

The first three terms of a geometric sequence are: 16 ; 4 ; 1 3.2.1 Calculate the value of the 12th term. (Leave your answer in simplified exponential form.) Calculate the sum of the first 10 terms of the sequence.

(3) (2)

3.2.2 3.3

1 1 1 1 Determine the value of: 1 1 1 1 ... up to 98 factors. 2 3 4 5

(4) [19]

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Mathematics/P1

5 NSC

DBE/November 2014

QUESTION 4 The diagram below shows the hyperbola g defined by g ( x) y = 1 and x = – 1. The graph of g intersects the

2 q with asymptotes x p x-axis at T and the y-axis at

(0 ; 3). The line y = x intersects the hyperbola in the first quadrant at S.

y

3

y=x g

S

1

T

x

1

O

g

4.1 4.2 4.3

Write down the values of p and q. Calculate the x-coordinate of T. Write down the equation of the vertical asymptote of the graph of h, if h( x) g ( x 5) Calculate the length of OS. For which values of k will the equation g(x) = x + k have two real roots that are of opposite signs?

(2) (2)

(1) (5)

4.4 4.5

(1) [11]

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S( 1 ; 2)

Mathematics/P1 6 NSC DBE/November 2014

f

QUESTION 5

1 Given: f ( x) log a x where a 0 . S ;1 is a point on the graph of f. 3

y

f

x

O

. S 1 ; 1

3

5.1 5.2 5.3 5.4 5.5

Prove that a 3 . Write down the equation of h, the inverse of f, in the form y = ... If g ( x) f ( x) , determine the equation of g. Write down the domain of g. Determine the values of x for which f x 3.

(2) (2) (1) (1) (3) [9]

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Mathematics/P1

7 NSC

DBE/November 2014

QUESTION 6 Given: g ( x) 4 x 2 6 and f ( x) 2 x . The graphs of g and f are sketched below. S is an x-intercept of g and K is a point between O and S. The straight line QKT with Q on the graph of f and T on the graph of g, is parallel to the y-axis.

y

f

g

Q

x

O K S

T

6.1 6.2 6.3

Determine the x-coordinate of S, correct to TWO decimal places. Write down the coordinates of the turning point of g. 6.3.1 Write down the length of x-coordinate of K. QKT in terms of x, where x is the

(2) (2)

(3) (6) [13]

6.3.2

Calculate the maximum length of QT.

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Mathematics/P1

8 NSC

DBE/November 2014

QUESTION 7 7.1 Exactly five years ago Mpume bought a new car for R145 000. The current book value of this car is R72 500. If the car depreciates by a fixed annual rate according to the reducing-balance method, calculate the rate of depreciation. Samuel took out a home loan for R500 000 at an interest rate of...

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